Nearest-Neighbor Qubit Grid for All-to-All Quantum Connectivity
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Solution Overview
Problem
The restricted connectivity of current quantum processors and noise in quantum hardware hinder the effective implementation of quantum algorithms for optimization problems, particularly those requiring all-to-all interactions, leading to a rapid dissipation of any theoretical quantum advantage.
Innovation Solution
Implement all-to-all connectivity in gate-based quantum computers using nearest-neighbor interactions by constructing a problem Hamiltonian, applying driving and problem Hamiltonians, and utilizing CNOT gates within a physical qubit grid, with parity check corrections and iterative processes to enforce qubit parities.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If quantum processors with restricted connectivity are used, then device complexity is reduced, but the ability to implement all-to-all connectivity required for optimization algorithms deteriorates
Solution Approach 1:
The patent introduces an intermediary encoding layer where classical variables are represented as quantum states through basis encoding. This encoding acts as a mediator that transforms the all-to-all connectivity requirement into a form compatible with restricted connectivity hardware, allowing optimization algorithms to be implemented on processors with limited qubit connectivity by mapping problem variables to quantum basis states.
2Device complexity
If quantum processors with restricted connectivity are used to emulate all-to-all architecture, then device complexity is reduced, but noise effects worsen and quantum advantage dissipates
Solution Approach 1:
The patent replaces the mechanical approach of physically connecting all qubit pairs (which would require all-to-all connectivity) with a computational approach using quantum basis encoding and measurement. Instead of relying on physical qubit connectivity, the solution uses quantum state representation and classical post-processing to achieve the same optimization functionality, thereby reducing sensitivity to connectivity restrictions and noise.
3Device complexity
If all-to-all connectivity is implemented through restricted connectivity hardware, then device complexity is reduced, but the number of operations and time required increases
Solution Approach 1:
The patent segments the optimization problem into quantum-encoded variable representation and classical measurement-based solution extraction. By encoding variables in quantum basis states and using measurement to extract optimization results, the method avoids the need for numerous sequential quantum operations that would be required to simulate all-to-all connectivity through restricted hardware, thereby reducing execution time.
Data Source
AI summary
A method for implementing all-to-all connectivity in gate-based quantum computers may include a classical computer program: receiving an optimization problem; constructing a problem Hamiltonian by assigning a qubit to each interactions between pairs of variables; associating each of the assigned qubits to a physical qubit in a physical qubit grid; assigning readout physical qubits in the physical qubit grid to neighbors of the associated physical qubits; instructing the quantum computer to apply a driving Hamiltonian and the problem Hamiltonian to the physical qubit grid; instructing the quantum computer to apply CNOT gates between associated physical qubits on edges of each triangle and square in the physical qubit grid and the readout physical qubits in centers of the triangles and squares; instructing the quantum computer to measure the readout physical qubits; and determining that the measurements of all readout physical indicates that parities between the physical qubits are enforced.